Question: The geometric sequence $(a_i)$ is defined by the formula: $a_i = -\dfrac{4}{3} \left(\dfrac{3}{4}\right)^{i - 1}$ What is $a_{2}$, the second term in the sequence?
Solution: From the given formula, we can see that the first term of the sequence is $-\dfrac{4}{3}$ and the common ratio is $\dfrac{3}{4}$ The second term is simply the first term times the common ratio. Therefore, the second term is equal to $a_2 = -\dfrac{4}{3} \cdot \dfrac{3}{4} = -1$.